Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: If d Q and d W represent the heat supplied to the system and the work done on the system respectively. Then according to the first law of thermodynamics d Q=d U-d W.
Reason R: First law of thermodynamics is based on law of conservation of energy.
In the light of the above statements, choose the correct answer from the options given below:

Solution

Physics sir · 4 steps

Watch the sign of work: work done on the gas is minus the work done by it, so the minus sign in A is right.

1. Usual form. The first law is usually written dQ = dU + dW_(by), where dW_(by) is the work done by the system. Heat supplied either raises the internal energy or leaves as work.
2. Switch the convention. Assertion A uses dW for work done on the system. Work done on the system is the negative of work done by it, so dW_(by) = -dW.

   dQ = dU + dW_(by) = dU - dW

3. Check Reason R. The first law is energy bookkeeping. Energy put in as heat must show up as a change in internal energy or as work, so no energy is created or lost. That is the law of conservation of energy, and it is exactly why the equation in A holds.
4. So. A is correct, R is correct, and R explains A. The answer is (b).

The idea to keep. Before you judge a first-law equation, check whether W means work by the system or on it. With W by the system, dQ = dU + dW. With W on the system, dQ = dU - dW.

Answer from the NTA final answer key. Solution by PrepWiser.